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Rotational Motion question

2007 · Shift 0 · Q94
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  5. /2007 · Shift 0 · Q94

Rotational Motion question

2007 · Shift 0 · Q94

JEE MainPhysicsRotational MotionMCQ+4 / −1
Angular momentum of the particle rotating with a central force is constant due to
  1. A
    constant torque
  2. B
    constant force
  3. C
    constant linear momentum
  4. D
    zero torque
View written solutionFree

Correct answer: D

  1. For a particle moving under a central force, the force always acts along the line joining the particle and the center.

  2. Torque about the center is τ⃗=r⃗×F⃗\vec{\tau} = \vec{r} \times \vec{F}τ=r×F Since for a central force, F⃗\vec{F}F is parallel (or antiparallel) to r⃗\vec{r}r, r⃗×F⃗=0\vec{r} \times \vec{F} = 0r×F=0 So, τ⃗=0\vec{\tau} = 0τ=0

  3. The relation between torque and angular momentum is τ⃗=dL⃗dt\vec{\tau} = \frac{d\vec{L}}{dt}τ=dtdL​ Therefore, if τ⃗=0\vec{\tau} = 0τ=0 then dL⃗dt=0\frac{d\vec{L}}{dt} = 0dtdL​=0 which means angular momentum L⃗\vec{L}L remains constant.

  4. Now check the options:

  • A: constant torque — incorrect, because constant torque generally changes angular momentum linearly with time.
  • B: constant force — incorrect, constancy of force does not guarantee constancy of angular momentum.
  • C: constant linear momentum — incorrect, not the reason here.
  • D: zero torque — correct.

Hence, the angular momentum is constant due to zero torque.

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